This has to be the underlying (correct) 'reason' because, otherwise one would have a reactionless force. How the air is deflected must also be for (correct) aerodynamic reasons. As with the concurrent discussion thread on How Aeroplanes Fly, people introduce a similar false dichotomy. Can't we maintain more than one ball in the air at a time (mentally)?I'm not aware of real world formulas. There are idealized formulas for spinning cylinders, but these are fairly off from actual real world examples.
Wiki article, the lift force related to Magnus effect is due to diversion of air flow in the wake that trails the spinning ball:
Another archived seperation of flow explanation: